"The left hand side" may be optionally used when we're talking about the real physical world. We wouldn't use the expression when referring to a direction, as in "Turn to the left," or "Take your second left"; but we'd use it for a locatiion: "The tuna fish is on the left hand side of the aisle," although it's certainly not required. " In such discussions, "the left hand side" is not appropriate, although the terms originated based on the arrangement of the two groups on the left- or the right-hand side of the aisle in the chamber in which they deliberated.
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